Can All Coefficients 'a' and 'b' Be Roots in Their Own Set of Quadratics?

[app_pp]

1. Homework Statement :
We have 'n' quadratics is the form x^2 +aix+bi
All values of A and b are different.
Is it possible to have all values of A and B as the roots of the n quadratics

2. The attempt at a solution:
Well. I know that all values of 'a' and 'b' must (if possible) be in one of the n (x-t)(x-s) where t and s are two values of a and/or b. I have proven that when n=2 its possible for all values, however i have difficulty with n>3

 

[chaoseverlasting]

Could you please clarify the question? Are there any other constraints to the question (like the roots must be real/complex)?

Why should there be a problem when n>3?

 

[app_pp]

Well there are no other restraints. Only all the values of a and b are different. I assume that both complex and real numbers are possible.

The answer to your second question I was having difficulty with N>3 is because there are not fixed 'positions' for each value